Slashdot Mirror
Classic Math Puzzle Cracked
An anonymous reader writes "This is cool - if mind-bending. A century ago, a self-taught math genius from India noticed some patterns in how numbers can be created by adding other numbers. Now a grad student has finished the job showing that the patterns apply to all prime numbers, not just some. There's more on the Indian math guy here."
you mean Srinivasa Ramanujan
Due to financial difficulties, the light at the end of the tunnel has been turned off.
Let's not use real names or give any credit to some guy.
More on Ramanujan at St. Andrews
Also at physorg.
It all deals with the Partition function.
The Indian mathematician outsourced this to a US grad student
"I'd rather be a lightning rod than a seismometer." -Ken Kesey
"Andrews says the methods used to arrive at the result will probably be applicable to problems in areas far afield from mathematics. He and Mahlburg note partitions have been used previously in understanding the various ways particles can arrange themselves, as well as in encrypting credit card information sent over the internet."
That's got to be the worst write up I've ever seen on /.
This statement implies that the genius is famous because he noticed that there is/are pattern(s) in how you can add up numbers to get other numbers . . . that statement is so vague that the discovery could be incredible or intuitively obvious.
Quoted from one of the links is a much better explanation below:
One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. The problem of finding p(n) was studied by Euler, who found a formula for the generating function of p(n) (that is, for the infinite series whose nth term is p(n)xn). While this allows one to calculate p(n) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p(n)).
Straight from the horses mouth... http://www.news.wisc.edu/10833.html I saw that a few days ago during the Nanotechnology article; I never thought of submitting it.
Would you kindly mod me +1 insightful?
His name is Ramanujan. You may just be trying to be cute by calling him "Indian math guy", but give him some props too. Hiding his name in the URL isn't enough.
That Ramanujan is refered to as `that Indian math guy'...
I thought this was news for nerds, sure maybe not everyone knows who Ramanujan was, but a good proportion should, at least enough that you don't have to demean him with a vague description.
a self-taught math genius from India noticed some patterns in how numbers can be created by adding other numbers.
yeah, I saw that too. Like, how if you have a 4, and add a 1, you get a 5. It's pretty cool.
"We would not have expected that the crank would have been the right answer to so many of these congruence theorems"
ah crank.. is there anything it cant do?
"Na-hee, na-na-jar. Na-hee-na-na-jar.
It's not that difficult."
"Yeah, well at least your name isn't Michael Bolton."
It is interesting that the New Scientist article basically attributes the idea of studying number partitions to Ramanujan, yet the linked article on him mentions that Euler had studied the problem before, and given a partial solution...
Repton.
They say that only an experienced wizard can do the tengu shuffle.
GH Hardy (he wrote A Mathematician's Apology) speaking of Ramanujan:
I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
(London 1940).
"The more you know, the less sure you are." - Voltaire
Not really. It only works if you are Muslim and male there. Pakistan actually has laws which include rape as a punishment for women, and the system also encourages killing of non-Muslims by specifically (in the code of law) making the killing of a non-Muslim a minor crime compared to the killing of a Muslim. I can provide links to both horrific laws if you want. That is not very intellectual or nurturing. Islam has absolutely no place in law, and any country that governs by Islamic law is declaring a war on those who don't worship the Muslim god. That is rather anti-intellectual. The same goes, of course, for any government that forces any religion on its people, including Christianity.
Don't blame Durga. I voted for Centauri.
... if you'd posted anonymously.
Infuriate left and right
The summary didn't name Karl Mahlburg, the subject of the article, either.
After just having seen a science guy, now we have an indian maths guy... Priceless :)
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
Or his mother cooked for him, and later his wife cooked for him.
sig
When I was a PhD math student, I often annoyed professors by asking them about real-world applications, and usually got vague answers like the one quoted.
Now, instead of becoming a math professor, I've been writing software for 20+ years, and about the only math I've found useful is of the "0xa + 6 = 0x10" variety. (And yes, I know that some math is useful.)
... that Ramanujan gets referred to on slashdot as the "Indian math guy" and is followed by jokes on outsourcing. You can read about him at http://scienceworld.wolfram.com/biography/Ramanuja n.html
or read the book "The Man who knew infinity" by Robert Kanigel.
He had remarkable contributions in number theory, all made
with very little formal training. His story cannot be explained
in any other way but supreme in-born genius (he himself explained it by inspiration from the goddess Namagiri).
The attitude to math in the general populace is one of total
avoidance. I had hopes that the average slashdotter was different.
I believe that the American Mathematical Society wrote up a nice review of his lost or last notebook a few years ago.
"sweet dreams are made of this..."
"patterns apply to primes" Does this mean to generate a/any prime number you can use a formula? If so does that mean it's easier to factor numbers?
So, do you think that opposition to forced Islam means opposition to Islam in general? Then there is the unjustified aggression and occupation by Pakistan against Kashmir. Kashmir never threatened or attacked Pakistan.
Don't blame Durga. I voted for Centauri.
Amen. One can only hope timothy will get kicked from the editor crew as soon as possible.
quidquid latine dictum sit altum videtur.
Well said. Now, watch for flamebait about "curry" and Indians stealing jobs from Americans.
Just remember the dying words of Uncle Sandeep
"With great curry comes great responsibility!"
Can I get an eye poke?
Dog House Forum
The coolest reference on Hardy's reaction to Ramanujan's initial letter is seen in a letter that was sent by Bertrand Russell to an acquaintance. It goes something like:
"Saw Littlewood and Hardy in a considerable state of excitement. They claim to have discovered a second Newton, a Hindu clerk working in Madras for 20 pounds a year...It's all secret now, of course. I feel excited to know this"
From: Ramanujan: Letters and Commenary
Bruce C. Berndt and Robert L. Rankin.
American Mathematical Society-London Mathematical Society.
The influence of socialism is a problem in India, which means that is government is too strong at the expense of the governed. Controlled prices for things are always bad news.
Don't blame Durga. I voted for Centauri.
"how numbers can be created by adding other numbers"... that sounds more like the observation of an American presidency guy.
While this allows one to calculate p(n) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p(n)).
The value was already known exactly. There was already a formula which could calculate it easily, and it had solid theoretical and empirical indications it was correct. Now we have a stringent proof. Big whoop.
Not to undermine its importance *in mathematics*. But I think we can safely say the world won't exactly change over this proof.
Kjella
Live today, because you never know what tomorrow brings
I was going to mention the Robert Kanigel book as well. It's a great book. You've beaten me to the punch.
Does this mean I've been wasting my CPU cycles?
Has the science guy's job been outsourced?
Not necessarily. He might just be an idiot.
hard core geek-ware
He didn't die from a "mystery illness", he died from tuberculosis (or as it was called back then, the consumption).
My digital rights don't need management.
"A decade ago, a self-taught computer genius from Finland [...] There's more on the Finish computer guy here."
(I think you get the point)
Bias or no, it's pretty hard to talk about a country being modern & civilized when the penalties for murder vary based on the religion of the victim.
Because your neighbor molests his children does not make it OK for you to 'merely' beat them.
my sig's at the bottom of the page.
Perhaps submitter-man was joking about indian-math-guy? Maybe it was an algebraic joke gone haywire? Ok, im reaching here but cut submitter-man a break, its tuesday. (dead-indian-guy doesnt care...)
Are you trolling?
If you are serious, could you provide some numbers, or facts that might substantiate your statement? Something that I could actually look at to compare between Pakistan and India. And while we're at it, let's add China to the comparison list. Let's restrict the data to things like number of scientists, amount of published research from both countries, things of that nature. Let's avoid listing "subjective points/opinions" that are not directly related such as politics, or social structure.
Only the civil code is non-uniform. This deals with marriage, divorce and inheritance, for instance.
A murder is a criminal case, and it is uniformly treated in the Indian Penal Code, irrespective of the usual divisions.
However, if you buy Lightning Shadow Software's new product, Vault Protector Pro Gold Platinum Edition, your data will be protected under uncrackable encryption and it will be 100% safe. Simply send an envelope stuffed with cash to my P.O. box address, which I will post here tomorrow, after I file the papers to form Lightning Shadow Software.
I had a friend from New York refer to the Alamo as "that church thing." How does anyone get through school without hearing about Ramanujan?
I would like to encrypt my credit card information for sending it over the Internet. Can someone *please* help me use this article to do that? I mean, where do I plug in the credit card number? Does it matter that mine doesn't end in "4" or "9"? Do I need the CCV?
It's always them. They always solve this stuff in college. They get famous...then drift off into obsucurity. Like the Indian guy. And, I hate math.
In America, you spam computers In Soviet Russia, computers spam you!
Seriously, the dude at 7-11 totally fucked up my change last time I bought a Slurpee.
In some ways the two made an odd pair
Not only were Ramanujan and Hardy an odd pair, but they were also a genious comedy duo!
I just pooped your party.
"Ramanujan had always lived in a tropical climate and had his mother (later his wife) to cook for him: now he faced the English winter, and he had to do all his own cooking to adhere to his caste's strict dietary rules." Wow.. I really think they could have worded that better.
The Pi symbol /. uses for Math articles is very appropriate in this case, because Ramanujan also came up with a formula for the numerical representation of Pi
That's the first thing I thought of when I saw the article text, and I was kind of disappointed it wasn't about that particular aspect of Ramanujan.
Show me on the doll where his noodly appendage touched you.
That's not the point. He is a person. He did something important. He has a name. He is NOT "the Indian math guy".
Ramanujan was one of the greatest mathematical geniuses of the 20th century. there are some people on./ who could do with some basic education.
I had hopes that the average slashdotter was different.
/.er is probably involved in some kind of IT work requiring certification but not a degree of any kind. There's nothing wrong with that, of course. It's just not the most likely description of someone who has a genuine interest in mathematics.
This is definitely a trollish thing to say, but why? Consider what the majority of stories are about. The average
I think he should be called a "Native American", or more specifically, his tribe, cherokee, apache, or iroquis.
But Indian? Welcome to 1875, Mr. Racist.
When I was a PhD math student, I often annoyed professors by asking them about real-world applications, and usually got vague answers like the one quoted.
Well, then don't go to the Pure Math department when you're asking questions about Applied Math! Don't go to the C&O department, and ask about Statistics, and don't go the Actuary Science department, and ask about Accounting! Yes, they're all within the Math Faculty, but you have to pick your department correctly, or you won't get the answers you want! Sheesh! You wouldn't go to a French professor, and get all annoyed that they didn't speak ancient greek, would you? They're in the Arts Faculty, but Ancient Greek belongs to the Classical Studies department, and French belongs to Romance Languages department.
There is a lot of mathematics out there with real world applications: modeling for physics and engineering, non-linear statistical methods for stock market analysis, all sorts of new crypographic methods and applications, graphical rendering engines; tons of stuff.
Typically, pure math is far in advance of real-world applications: most of the mathematics we use today had no "real world" application when it was first concieved of. Field theory was considered "useless" when it was created, but it forms the heart of both modern cryptography, and of error correcting codes. These two, in turn, have become crucial to the success of our banking and telecommunications industries.
New insights into eliptic curves are yielding a new form of cryptography; the discrete logarithm problem forms the basis of another. Ten years ago, quantum computing was a matter of purely speculative mathematics; today, it exists as an experimental science.
Imaginary numbers were so named because no one figured they had real world uses: today, they're taught as a practical matter for electrical engineers to use in their electronics calculations. Taylor series approximations take the guesswork out of sin and cosine calculations, polynomial interpolation techniques allows computation of a "curve of best fit" for arbitrary scientific data, and every modern engineer is now aquainted with Fourier's transform. Some of Benoit Mandlebrot's notions about fractals were used to create JPEG compression, in common use on the Internet. Wavelet theory is currently being developed to attempt to improve on current methods.
Math is pushing ahead very fast; the real reason you don't usually see it is because it's often right at the heart of things; deep inside our hashing algorithms, hidden in a cryptography library, working behind the scenes as the statistical underpinnings of a successful greylist design that keeps spam away. It's in the boolean algebras that were used to design an efficient circuit layout, and in the iterative methods used to compute a new airfoil design. It's everywhere.
--
AC
Especially those of us who think this place is called Dotslash. ;-)
How can you use my intestines as a gift? -Actual Hong Kong subtitle.
I suppose Evariste Galois was just some guy who flunked his entrance exams and was killed in a duel when he was 20? What would you have to say about Paul Erdos?
(snicker)
You're putting Linus in the same crowd as Einstein and claiming Ramanujan is "some grad student"?
Keep'em coming. I needed a good laugh. We'll see how long it takes for my ribs to hurt. You have a long way to go to top the time in college when we crumbled Gaines Burger dog food and put it into the salad bar, but with some work and a good mentor, you too, might be funny.
Wait, I almost forgot. Are you trolling?
bwahahahahahahahahahahahaha
to plug my sig. Really, I can't fathom how people would choose primes over protiens when protiens may help the fight against cancer amongst others. Please follow the link at least and take a look.
Your CPU is not doing anything else, at least do something.
State your source.
Why Vegan? No other food choice has a farther-reaching and more profoundly positive impact on all of life on Earth.
Excuse me for not being a Linus fanboy, but Linus is NOT in the same league as Einstein. I'm surprised they're mentioned in the same sentence. When Linus dies, nobody will be falling over themselves to dissect his brain.
Any slashdot cyrpto gurus want to take a stab as to what implications this has for cryptogrphy and factoring large numbers?
Now, than can be described as:
tasks(723) drafts(105) languages(484) examples(29106)
"All you've learned was that Ceasar was a salad dressing dude."
and:
"If I was a short French dude from the past where would I go?"
These posts express my own personal views, not those of my employer
Awww shrucks! :)
But when your number's up...
Ludwig Wittgenstein
"I find your lack of faith disturbing."
"Never underestimate the power of the [fans]."
Elvis is a good example of the strange things people will do for a dead guy. (Except, he's not really dead, right?)
Exam 4/C again. Maybe I'll do better this time.
Well, then don't go to the Pure Math department when you're asking questions about Applied Math!
The question to pure mathies might have been phrased: "What have the Applied Math people done with your past discoveries in this sub-field?" In the case of number theory and other discrete fields of study (pardon the pun), discoveries have so often led to something or other regarding cryptography or cryptanalysis or both.
Probably the chick with the huge... eyes... who always sat next to him in class.
Somebody's been watching too much anime.
NOT in the same league as Einstein or Linus Torvalds
Funny that your parochial flamebait happens to be true. Ramanujan was definitively smarter than either of them.
Not to put down Big Al, but he only had a small armful of memorable discoveries spread over the decades of his career. OTOH, Ramanujan pumped out astonishingly brilliant stuff pretty much every day of his sadly brief adult life.
Yeah. I was waiting for the part where the tigers turned into butter.
Don't blame Durga. I voted for Centauri.
But I think we can safely say the world won't exactly change over this proof.
A proof that a formula is correct clears the way for the formula to be used in applied mathematics. A lot of the discoveries in number theory go toward making and breaking ciphers, and RSA and DH public key systems wouldn't have been possible without a few prime number theorems.
Less, so, than Islam. When is the last time that the India criminal justice system imposed a sentence of rape on a woman? Yet, Pakistan's government did this a couple of years ago (The national government only arrested the rapists after strong international pressure, but then released them, thus approving of what they did). However, if your point is to make Pakistan's unjust system look good by saying "see, they are worse!", why don't you cut to the chase and bring up North Korea and the Spanish Inquisition? Pakistan is not as bad as either of those two examples, so by golly it sure must be swell! End of argument.
Don't blame Durga. I voted for Centauri.
I could not agree more.
Mathematics at this level, in my naive opinion, is almost an art form, in that it uses unscientific methods to reach scientifically provable results. And in so doing, it reveals volumes about the method of knowledge.
I've spent countless hours playing with calculators watching for patterns. I once worked at a job that left me sitting at a desk for hours with nothing to do but think, and playing with numbers never failed to fill the time with amusing discoveries of how numbers could produce unexpected symmetries and results.
While I did quite well in prep school in mathematics, my love for mathematical symmetry morphed to the study of music theory in college (the two are not as dissimilar as most would think).
There are beauties to be found in numbers, in pure mathematics. It is nothing short of the study of the world around us as expressed in purely intellectual form. At the highest level, I would not be surprised if the observations turn inward toward the observer, if the discoveries tell us more about how intellect works as it understands quantization than about the actual numbers at play.
This "Indian math guy" would have been one hell of a guy to have dinner with. What I'd do to be inside his mind for just a short time!
Don't mock or belittle that which you don't understand. To do so often reveals more about yourself than you probably want revealed.
But if we use negative integers, 1729 gets trumped by 0, since x^3 + (-x)^3 = 0 for all integers.
As a math graduate student student I was invited to watch the presentations of the people applying for a graduate faculty position at the university. I was only able to make it to one of the presentations, but it was an unforgetable experience for me.
The applicant gave a very interesting presentation. I got lost during the first 5 minutes when he was still giving background, but it was still interesting. His presentation was on - assuming that I remember any of the very little that I may have understood - some specific behaviors of the infinite boundaries of n-dimensional manifolds.
The best part was when he said, "In case you think that this is just esoteric and 'out there,' I want you to know that this stuff has real applications in topology."
There were about 6 other grad students and 15 math faculty there and I think I was the only one to notice how funny that was, so I'm sorry if you don't get the joke.
Exam 4/C again. Maybe I'll do better this time.
Having seen the work of all three, and met one of them, I'd have to say that he was significantly smarter than Albert or Linus.
--MarkusQ
From the writeup I know know that "some Indian math guy" did something about "how numbers can be created by adding other numbers".
News for nerds indeed. The man is one of the most well-known mathematicians there is (as much as a mathematician can be well known). The guy even has a number named after him, 1729.
That article also has a lot of fun Futurama references too.
I know why you defend Pakistan, even the government is wrong about things and engages in religious oppression. Read Article 19 of your Constitution. It is even illegal for you to look at Islam with an open, critical mind: press freedom must only be for "the glory of Islam". I understand why you say this stuff now. No honest person would make these claims on their own.
Don't blame Durga. I voted for Centauri.
In theory there is no difference between theory and practice. In practice there is. - Yogi Berra
From TFA:
the number of partitions for any number ending in 4 or 9 is divisible by 5
Please forgive my non-mathmatician question, but when I think of numbers I don't think of them as 'ending' in anything in particular. If we were to use a unique symbol for every number (the way I see them in my mind), how would this change the description of these patterns? If we were to write everthing in hex would there be other interesting patterns?
Einstein == Genius
How can you say Linus Torvalds is a genius though? The guy developed an operating system. He was not the first, he will not be the last. Were any of his developments major leaps forward in technology requiring a major insight nobody else had?
To be honest even RMS, love him or hate him, is closer to genius than Linux as he has shown a greater leap by pushing the concept of free software - a previously unheard of concept. This required thinking outside the norm.
But, in the US not all murders are equal under the law.
If someone from a protected minority group is killed it can be much more seriouis than a non-minority murder because of "hate-crime" laws.
These laws basically say that the minority status of the victim and the personal beliefs of the murderer affect the seriousness of the crime.
Years from now this will either have blossomed into more comprehensive thought-control laws, or be laughed at.
Exam 4/C again. Maybe I'll do better this time.
holy self-indulgent tripe batman.
I agree with the literal thing you are saying, however.
Sigs are awesome huh?
His name is in the first sentence.
I just moused over, and it's in the freaking URL.
The best general reading about applied math in the context of Ramanujan's work and life are in G.H. Hardy's A Mathematician's Apology and Robert Kanigel's The Man Who Knew Infinity. Both are excellent reads for non mathematicians.
India has a very long history of mathematics. eg. Pythagoras theorom was proven in India long before Pythagoras was even born.
Engineering is the art of compromise.
This sounds like it was posted by a Seventeen reader. A new low for /.
Is it not possible for moderators to edit the post? I know slashdoters hate sensoring, but come on people let's show Srinivasa Ramanujan a little respect.
Those who would like to learn more about the "Indian math guy" should read the excellent biography, The Man Who Knew Infinity".
Almost as interesting is looking into how much human coaching AM took to come up with the results - its not all that clear how much human intervention was involved, but I've certainly heard AI researchers cast a nasturtium or two on AM (and its successor Eurisko) because the results were essentially unreproducable.
Actually, TFA is really annoyingly written. To paraphrase: "Ramanujan noticed that most numbers can be expressed as sums of other numbers." No shit, Sherlock. While that wasn't what he "noticed" about numbers at all, _New Scientist_ puts a large emphasis on it so they can segue into the concept of partitions. The author needs to be dragged out into the street and beaten.
God, Zues, even "Mormon Smith" has more relavant google hits.
Not a troll, just what did Namagiri do before this Math Guy came along?
This issue is a bit more complicated than you think.
That said, my guess is that the poster had copied the URL of the story and couldn't remember how to spell Ramanujan, and just used some shorthand which came off as a slight where one wasn't intended. The myriad of inevitable offshoring jokes are much more offensive than the (correct if somewhat lame) description of Ramanujan as an "Indian math guy."
Dude, I think I can see my house from here.
While I did quite well in prep school in mathematics, my love for mathematical symmetry morphed to the study of music theory in college (the two are not as dissimilar as most would think).
That's certainly true.
How's this for a strange coincidence.
It would be tough to name the greatest mathematician, or the greatest composer of all time since there is a great deal of subjectivity to that.
However, I believe that it's pretty generally accepted that the greatest musical dynasty was the Bach family and the greatest mathematical dynasty was the Bernoulli family.
There were at least 3 generations of some of the greats in their respective fields.
They lived at the same time, and within 100 miles of each other.
I'm not saying it means anything, but it truly amazed me the first time I learned about it.
Not to put down Big Al, but he only had a small armful of memorable discoveries spread over the decades of his career.
You are kidding, right? Sure, as Einstein grew older, he produced less and less, but here's what he did in 1905 alone:
"A New Determination of Molecular Dimensions" (Einstein's doctoral dissertation) (30 April 1905)
Buchdruckerei K. J. Wyss, Bern, 1906.
Also: Annalen der Physik, 19(1906), pp. 289-305.
This is Einstein's doctoral dissertation, submitted after much delay to the University of Zurich. In it he uses available physical data on the diffusion of sugar in solution and the effect of dissolved sugar on the solution's viscosity to determine the size of sugar molecules and Avogadro's number. The analysis makes the kinetic theory of heat more definite, in so far as it provides a measure of the real size of molecules, so that they cannot be dismissed as easily as useful fictions. It is the least impressive of Einstein's work of 1905 although, curiously, the most cited.
"On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." (Brownian motion paper) (May 1905; received 11 May 1905)
Annalen der Physik, 17(1905), pp. 549-560.
In this paper Einstein reports that the kinetic theory of heat predicts that small particles suspended in water must execute a random motion visible under the microscope. He suspects this motion is Brownian motion but has insufficient data to affirm it. The prediction is a powerful test of the truth of the kinetic theory of heat. A failure to observe the effect would refute the theory. If it is seen and measured, it provides a way to estimate Avogadro's number. The domain in which the effect is observed is one in which the second law of thermodynamics no longer holds, a disturbing result for the energeticists of the time.
"On the electrodynamics of moving bodies" (special relativity) (June 1905; received 30 June 1905)
Annalen der Physik, 17(1905), pp. 891-921.
Einstein develops the special theory of relativity in this paper. His concern, as he makes clear in the introduction, is that then current electrodynamics harbors a state of rest, the ether state of rest, and the theory gives very different accounts of electrodynamic processes at rest or moving in the ether. But experiments in electrodynamics and optic have provided no way to determine which is the ether state of rest of all inertial state of motion. Einstein shows that Maxwell-Lorentz electrodynamics has in fact always obeyed a principle of relativity of inertial motion. We just failed to notice it since we tacitly thought that space and time had Newtonian properties, not those of special relativity.
"Does the inertia of a body depend on its energy content?" (E=mc2) (September 1905; received 27 September 1905) Annalen der Physik, 18(1905), pp. 639-41.
Written as a brief follow-up to the special relativity paper, this short note derives the inertial of energy: all energy E also has an inertia E/c2.
"On a heuristic viewpoint concerning the production and transformation of light." (light quantum/photoelectric effect paper) (17 March 1905)
Annalen der Physik, 17(1905), pp. 132-148.
While the victory in the 19th century of the electromagnetic wave theory of light over Newton's corpuscle view is undeniable, Einstein shows that its success is incomplete. The theory gives incorrect results for the analysis of heat radiation. He looks at the thermodynamic properties of high frequency heat radiation and finds that this radiation behaves just like a collection of many spatially localized units ("quanta") of energy of magnitude hf (h=Planck's constant, f=frequency). He proceeds to show how this quantum view of light makes sense of several experiments in electrodynamics and optics, the best know being the photoelectric effect. He then described the paper as "revolutionary."
And these were on wildly different apsects of physics -- Brownian motion, Relativity, Statistical Mechanics, Photoele
"That's not even wrong..." -- Wolfgang Pauli
http://members.cox.net/xocxoc/humor/anyquestions.
My favorite question from the list:
"sweet dreams are made of this..."
I just want to say... INDIA ROCKS! Okay, let me stop the Nationalism >.> I think that Srinivasa Ramanujan deserves the same respect that Einstein and Torvalds does, which is the mutal respect humans have for people who make great strides in various fields. (One may argue that Torvalds hasn't done too much...but I don't want to start a flamewar).
Current State: Pirates > Cowboys + Ninjas + Robots Yarrrr
</sarcasm>
I was just wondering that myself
Want to find other gamers to play board and role playing game
A wonderful biography of Ramanujan is, "The Man Who Knew Infinity: A Life of the Genius Ramanujan", by Robert Kanigel
It's really interesting. Ramanujan was doing all this brilliant number theory on his own in India, and he decided to start sending his ideas around. He contacted several brilliant mathematicians, none of whom could figure out what he was talking about, largely because Ramanujan had some peculiar ways of expressing things. Finally Ramanujan contacted G. H. Hardy (at Cambridge), who saw his potential. Hardy invited Ramanujan to come to Cambridge right away, but couldn't get him to come because Ramanujan was a devout Hindu, and felt that he would be permanently "polluted" were he to leave India. Eventually, Ramanujan came to an agreement with his mother and went to spend time with Hardy, who spent a great deal of time helping Ramanujan convert his raw ideas into a more traditional, presentable form for maths journals. Ramanujan had a tough time in Cambridge, because he really didn't fit in. Eventually, he became very sick (tuberculosis, I think), and died. My understanding is that serious mathematicians are continuing to gather many new ideas in number theory from Ramanujan's notebooks, which are published by Springer-Verlag.
If you watch TV news, you know less about the world than if you just drank gin straight from the bottle.
University of Minnesota on April 1, you could go to the
Spring 2005 Combinatorics Seminar
Friday at 3:35, Vincent Hall 364
April 1:Karl Mahlburg University of Wisconsin
The Andrews-Garvan-Dyson crank and proofs of partition congruences
Abstract: In 1944, Freeman Dyson conjectured the existence of an integer-valued crank function for partitions that would provide a combinatorial proof of Ramanujan's congruence p(11n+6) \mod{11} = 0 by dividing the partitions of 11n+6 into 11 classes of equal size. Forty years later, Andrews and Garvan successfully found such a function and proved the celebrated result that M(m,11,11n+6) = p(11n+6)/11, where M(m,N,n) is the number of partitions of n for which the crank is m modulo N. The main result of this talk proves a conjecture of Ono, which essentially asserts that Dyson's elusive crank is a universal combinatorial statistic that ``explains'' partition congruences of every known type.
N/T
------ The only greater hazard to your liberty than n politicians is n+1 politicians.
We could even toss in Linus using x86 assembly language. Aye, there's a contest to behold.
By the same token, "German guess guy" is Heisenberg, "Italian nuke guy" is Fermi and "Slashdot condescension guy" is whoever bespoke "Indian math guy," referring to Ramanujan. Mathematics, made of pure thought, advances meteorically faster than the dull material world, let alone the moral, spiritual or (shall we call a spade a spade?) ethological world of semi-sentient apes and slash dotters. Ramanujan lived in a future virtually all of us cannot even imagine, and his name is revered, not because we understand him, but because he thought the future beautiful.
``Tension, apprehension & dissension have begun!'' - Duffy Wyg&, in Alfred Bester's _The Demolished Man_
I've never heard of him, yet completed 3 semesters of calculus differential equations and some signal processing classes that are very math intensive and yet I've never heard of him and I don't "live under a goddamn rock" either.
Comment removed based on user account deletion
Thanks for the FUD, asshat. Ramanujan died of tuberculosis.
I've misplaced my copy of Ramanujan's biography, "The Man Who Saw Infinity", but I seem to recall that the anecdote attributed the quote about the number 1729 to Hardy's collaborator, J.E. Littlewood, in his later years, not to Ramanujan.
Hmm? I was just commenting on the extremely vague description of the article in agreement with the parent.
It had nothing to do with the fact that Ramanujan was indian or anything like that.
You beat me to it. I read the book several years ago, and it is well-written and exceedingly fascinating, and not just because of Ramanujan's poignant life, but because it is also the story of G.H. Hardy, and to a lesser extent, Hardy's collaborator, J.E. Littlewood. It is particularly notable for the descriptions of Ramanujan's life in south India as a devout, high-caste Hindu with a somewhat simple worldview, and the contrast with the Cambridge academic life of the handsome, urbane, and eccentric Englishman. Best of all, it is the story of the remarkable, unlikely collaboration between the wild talent Ramanujan, the "Prince of Intuition", and the rigorous Hardy, the "Apostle of Proof". It also conveys something of the excitement felt when Ramanujan burst on the scene, and offers a layman's glimpse into the rarefied circles of mathematical theorists. I highly recommend Kanigel's biography of Ramanujan to anyone looking for a good read, not just those interested in Ramanujan or mathematics.
Ramanujan's caste(clan) treated him as an outcast for traveling abroad. that contributed to his death.
:
from wolfram
Unfortunately, Ramanujan's health deteriorated rapidly in England, due perhaps to the unfamiliar climate, food, and to the isolation which Ramanujan felt as the sole Indian in a culture which was largely foreign to him. Ramanujan was sent home to recuperate in 1919, but tragically died the next year at the very young age of 32.
Furthermore, you know zero about nutrition if you believe that you'll suffer from vitamin deficiencies if you don't eat animal products. Disclaimer: I love rare steaks.
Einstein was very smart.
I wouldn't want to put him down.
But I agree that Ramanujan was a phenomenon. He was so completely different from any of his contemporary mathematicians that there is really no comparison.
He was discovered by the west when he sent a manuscript to Hardy, a famous English mathematician. Hardy almost discarded it, since much of it was stuff he had seen before (though Ramanujan had rediscovered it independently), but it also contained 120 thereoms no one but Ramanujan had ever seen before.
Later, when he came to England, Ramanujan filled notebooks with thousands of theorems, though not, apparently with proofs. I think proving Ramanujan's thereoms is still a major occupation of academia.
Interestingly, there is a similar story involving Einstein. Bose, who was an unknown Indian physics instructor, sent an unsolicited manuscript to Einstein which eventually led to the theory of Bose statistics, or Bose-Einstein statistics and the Bose condensate.
Crackpots from all over the world were sending Einstein manuscripts, and Bose's manuscript looked a lot like one of these. But Einstein read it anyway, and saw that Bose's ideas had merit. Ultimately, it seemed that Bose only had the one really good idea in him, and after collaborating with Einstein on the one paper, he went back to India and continued teaching. Apparently he was an especially good teacher.
MM
By including this sig, the copyright holders of this work or collection unreservedly place it in the public domain.
Now start to get your head around this... what if numbers are just, well, *human* constructs. As hard as that is to get your head around, think how easily that little concept completely changes your view of things.
If numbers are human constructs and nothing "inherant" in the universe, then the patterns that we find are not that unexpected. Humans are pattern hunting machines.
"Your superior intellect is no match for our puny weapons!"
I go to the grocery store and the bill for my beer comes to $2.56.
"Oh, two fifty six." I smile to the cashier, "That is the number two multiplied by itself eight times!"
She gives me that look like she's not sure if she calls security that they will have me on the floor at gunpoint before I explode.
You Americans, you know that look. Someone gives it to you every day.
Linus himself has been on public record at multiple occasions saying that "operating system code is nothing that is invented and that he is not an inventor.
the macintosh asterisk mailing list http://www.astm
By an amazing coincidence, Bill Gates is the Start (menu) guy!
But this is slashdot. Would it be wise to except any kind of sense here?
(Linus is an asshole. Yeah, he's cool, but he IS NOT A GOD.)
I don't understand why Pakistan is "glued" to India whenever the word India is mentioned. Though we are similar looking people, we just don't have anything in common. Except the skin colour, we have absolutely nothing in common. We are very very different from the Pakistanis.
In what context did you hear of him?
I assume these numbers are added to numbers to create (astonishingly) numbers. And this operation can even be applied to all prime numbers! This is really mindbending and puzzling and probably innovative too. Is this method patented yet? Hey, i got a great idea: let's use the "+" sign for this operation, something like "+(number1,number2)", i think i'll patent that.
Maybe that anonymous reader should've freed himself from the mindbended state briefly and taken the few extra seconds to specify "numbers" for the benefit of the readers.
"By the way if anyone here is in advertising or marketing... kill yourself." -- Bill Hicks
The flip side of this, is that, we are also pattern *makers*: that's why we perceive a picture of the Virgin Mary on a cheese sandwich, or once, in the heavens, constellations as patterns of stars.
When all you are is a pattern hunting machine, though, everything looks like a pattern. Try not to be paranoid -- some apparent patterns really AREN'T.
DNA is a Turing machine. You, however, being dynamic and emergent, are not.
Comment removed based on user account deletion
Not to put down Big Al, but he only had a small armful of memorable discoveries spread over the decades of his career.
;)
Only on Slashdot would there be a dude who argues that _Einstein's_ number of discoveries was mediocre
Relative to other geniuses, of course... *ow!*
Cheers
Stor
"Yeah well there's a lot of stuff that should be, but isn't"
What's up with that? So they only have names when they're American scientists? Do you know how much Srinivasa Ramanujam contributed to math??? Just because YOU don't know them does NOT make them any less deserving of the respect they SHOULD get from everyone for their contribution to the field!! Or are you just another one of those hicks who respects people based on their nationality and on rubbish like "if i don't know them, they're not worth knowing"?
Have some decency. Recognize genius and respect it. What have you accomplished? Even 1/10th of what any respected scientist has? Don't you expect people to call you by your name and not "hey you"? Why not give the same respect to others?
I'm also surprised that the Slashdot editors let this story be published without correcting it!! What, are story submissions now governed by a perl script?
RANT OFF.
Find a job you like and you will never work a day in your life.
If you took number theory or some high level mathematics courses and never heard about Srinivasa Ramanujan it would be akin to studying relativistic physics and never hearing about Albert Einstein .
Most people probably heard about Ramanujan recently from the movie "Good Will Hunting". Where they refer to Ramanujan by name several time during the movie, although they totally butchered his name and made me cringe every time they said it. The movie is based on a Ramanujan type character, in Hollywood fashion though. Where a young good looking confidant and outgoing Matt Damon with the physique of a construction worker plays the math genius. Ramanujan was shy, introvert, awkward and not in the best physical health.
Even if Bose had only one good idea, he still did better than most of us. Plus a good teacher, especially in the 'hard' subjects, isn't to be sneered at eigther. Not that you seemed to be putting him down.
Mycroft
https://signup.leagueoflegends.com/?ref=4c3ed6600b6ea
Einstein was an intelligent man, but there are some doubts about how much stature to accord him. Perhaps you missed the PBS examination of the role his wife played in developing those early ideas, and perhaps you've ignored the more serious accusations leveled against him.
There's no doubt, however, that his importance to anti-Nazi propogandists deserves considerably more comment than it has received.
Mir Sultan Khan arrived in England in 1929 as manservant to an Indian Maharaja, and immediately took the European chess world by storm (the Wikipedia article compares him to Morphy). He convincingly defeated all the great players of that era -- Alekhine, Capablanca, Euwe, Rubenstein, more, but when the American master Reuben Fine visited the maharaja's digs in London, Khan was the waiter who served the meal. In 1933, the maharaja left England and Khan was taken back to India: no more tournament chess for him.
His story is not the same as the story of Blind Tom, in spite of cetain similarities. There is no indication that Khan's owner/employer exploited those remarkable talents, and the talents were in fact measurably remarkable. In the case of Blind Tom, one is tempted to think of S. Johnson's remark: "Sir, a woman's preaching is like a dog's walking on his hind legs. It is not done well; but you are surprised to find it done at all." [from Boswell's Life of Johnson]
Language Log refers to these constructs as "Snowclones", and cites several examples.
... to see low intensity racism having still supporters in /.
Heartwarming.
IANAL but write like a drunk one.
...that with a compression algorithm that claimed to compress _any_ file, you could just keep feeding its output back into itself, effectively allowing the reduction of _any_ file to 1 bit.
Which is clearly not possible.
IANAGOC (I am not a guru of cryptology). I think what this means is that you can tell a skimpy clad up-for-it busty prime number from a mile away. Traditionally you had to weigh, measure, calculate etc to tell if a prime was really a hot young chick and not a result of 10 pints of alycyhol. Now just by looking at what congruence each number gives you can judge whether its a prime or not. (I can't say for certain because the article is short on details of what these patterns are.)
I don't really know what method of cryptanalysis is used for breaking the RSA, but suppose if you can weed out the non-prime numbers you can drastically reduce the amount of calculations needed.
If you know better and think I'm wrong please do correct me and join in the discussion before any damage is done.
QOTD at the bottom of Slashdot's page, as I'm reading your comment:
"I gained nothing at all from Supreme Enlightenment, and for that very reason it is called Supreme Enlightenment." -- Gotama Buddha
Marx used the terms communism and socialism almost interchangably. The Soviet Union was made up of socialist republics (see the first S in USSR). However, in general usage, "communism" tends to be used for only the more extreme version of socialism.
Don't blame Durga. I voted for Centauri.
I first heard about him when I read Hardy's A Mathematician's Apology. A great read. Also heard about him when I took number theory.
JOIN US FOR PONG!
Wikipedia has its own version of the blind slave pianist:
http://en.wikipedia.org/wiki/Blind_Tom
-- Juanco
Only after international outrage and pressure.
"Which does not suggest to me that it condones such an act in any way."
You are right. The death sentence does not suggest that the Pakistani government condones it. The fact that all of the rapists were released from prison? Set free? That shows that the Pakistani government condoned the act.
Don't blame Durga. I voted for Centauri.
Really, I can't fathom how people would choose primes over protiens when protiens may help the fight against cancer amongst others. Please follow the link at least and take a look.
Contrariwise, I can't fathom how people would choose proteins over primes when primes may help the fight against identity theft amongst others. Please follow the link at least and take a look:
RSA Factoring Challenge FAQ
OK, so I'm an idiot in maths, and I've read about prime numbers and cryptography and how predicting prime numbers can help crack encrypted material, so is this development of any significance with cryptography?
I would even venture to say that Pakistan is an illegitimate entity. It broke from India in that war in order to deny basic human rights. The official name of the country is "Islamic Republic of Pakistan", which is an open declaration of war on Pakistanis and their right to make their own religious decisions.
Don't blame Durga. I voted for Centauri.
And if so, could this proof be of any practical value?
Well, I realized that if you multiply any number by 4, you can represent the total as a sequence of odd numbers. Actually, there's more than one sequence if the original number is not prime. One is obviously half the sum plus/minus 1. The other is longer. For example, 21*4 = 84 = 9+11+13+15+17+19. So, where's my /. article?
The previous comment is purposely vague and generalized, but all of the facts are completely true.
Random theory: perhaps this is related to the bike shed effect. The observation for this effect is that "getting permission to build a billion-dollar atomic power plant is easy, but a proposal to build a cheap bicycle shed will founder under the weight of endless discussion." This is theorised to be because "an atomic plant is so vast, expensive, and complicated that people cannot grasp it, rather than try, they'll fall back on the assumption that somebody else checked details before it got that far. However, everyone knows all about bicycle sheds, and feels no inhibition against debating their pettiest details without limit."
Perhaps more people work on diffusion effects of sugar in water because this is a more down-to-earth thing to think about drinking your coffee in the morning...
Relax, it's a joke. It's an ironic poke at the ignorance of slashdot. Sorry if it was too subtle for you.
And apparently you don't know everything about your own country (I'm assuming you're Indian). Sati has been illegal, not for decades, since 1829. That's coming up on two centuries.
Look, I understand why you're defensive. There is a lot of bigotry on slashdot, especially towards Indians. Many people's livelihoods are threatened. Ironically, many who are ardent capitalists are the most threatened, and the most bigoted. I guess when your political principles are based on "enlightened self interest" it's easy to conveniently change them when the outcome doesn't serve that self-interest.
Outsourcing is a bitter pill to swallow, but I believe we should take our medicine if we want to stay competitive. We've had it so good for so long that we now believe it's our right. Guess what? It's not. Our opulent (and sometimes even decadent) lifestyles have made us soft and lazy, and competition is hard and takes a lot of work. I'm confident we'll meet the challenge, but not until after a lot of pain and adjustment. A lot of Americans will suffer, and are suffering. However, a lot of suffering goes on throughout the world, and we have no right to think we are somehow immune because we are Americans.
It's not surprising that we put a gang of criminals into power, because Americans are in love with the ideology of capitalism and the criminals talk a good game of capitalist ideology. They want to destroy what safety nets we have while at the same time engage in a huge give-away to their closest friends and allies. And we go along with it because we don't understand the principles of capitalism, but are mesmerized by the ideology in the same way that compulsive gamblers are mesmerized by the lottery. We've become brittle, when we need to become more flexible.
Personally, I want to move to Mexico, because that's where the jobs are going to be in ten years, and the cost of living is much cheaper. I don't want to wait too long, because eventually Mexico will try to close the border to prevent too many gringos from sneaking in.
It's not offtopic, dumbass. It's orthogonal.
The grandparent post's logic is incorrect. You cannot just reduce the bases that way and hope to get anything meaningful. In fact look at the original statement and take the case of the number 4. It has the trivial partitions of:
4
1 3
2 2
1 1 2
1 1 1 1
There are 5 of them, which fits the bill of being divisible by 5. Now the grandparent poster thought he saw a pattern by reducing to base two but in order for his claim to hold he had to change it so that it was the sum of all SMALLER numbers. That should have been the tip-off that something was amiss.
What would you have to say about Paul Erdos?
You know... that coffe drinking homeless guy who did a little math.
[my Erdos number=3]
-30-
madcity rocks the house again.
I knew Erdos first-hand - spent a brief time while I was in high school - studying with him at Indiana University (Bloomington, Indiana) in the late 70s and with Douglas Hofstadter at roughly the same time.
Several years later, I was at a math conference (as premed) and he walked up to me and started talking about some of the things I'd proposed. The profs I was with almost wet their pants just because I knew him, let alone that he knew me or had interest in things I'd discussed with him years ago (in high school)
"I'm also surprised that the Slashdot editors let this story be published without correcting it!! What, are story submissions now governed by a perl script?"
Unlikely.
I, for one, have considerable confidence that a fairly simple perl script could at least competently produce basic English spelling and grammar.
That's awesome!
Back in my undergraduate days, I actually worked on a similar problem to this at the Rose-Hulman REU. I initially thought that the theorem he proved was the conjecture we put at the end of our final writeup, but it sounds like he proved something else, sadly.
The Ramanujan congruences are incredible bits of number theory. They're pathetically simple to explain to the lay-person, but often take some ingenious logical and mathematical work to prove them. I learned so much about other higher-level mathematics during that REU than I would've in any one class in graduate school.
-Jellisky
You are correct, I incorrectly generalized the result. From the result, we know that there should be some pattern (two is a prime, and the proof is that such a pattern optains for all primes), but my off-the-cuff guess as to what it was is clearly wrong.
--MarkusQ
I was wrong, but not quite as wrong as you make it sound.
First off, ignoring the trivial partition just changes the parity, which would not affect any even/odd pattern beyond reverting the sense ("always even" <--> "always odd"). Using a trivial isomorphism is hardly a "tip-off that something is amiss".
Secondly, two is a prime and the proof in question AFAIK applies to all primes not just odd primes. The whole point of the discovery is that you can "reduce the bases that way" and you are guarenteed to "get something meaningful." So there is some pattern to the partitions of odd vs. even numbers, modulo some base, I was just incorrect in guessing what it is.
--MarkusQ
"What a complete joke of a post, rape as a punishment? What are you waffling about? Are you so blind that you believe everything you hear on TV?"
What does TV have to do with this? I read this from Pakistani sources. Even the Pakistani "patriot" who posted the parent item knows about it.
"Obviously, there is a war going on with the Muslims right now, obviously, negative propaganda about them will be encouraged."
"Propaganda" defined by you as information you don't like and would want to keep secret.
"I remember studying British Propaganda about the Germans in World War 2"
And I remember studying the Crimean war. But what does either entirely irrelevant situation have to do with anything? Oh wait. Your example is connected a little: like WW2 Germany, Pakistan is governed by a military dictatorship that has a foreign policy goal of exterminating Jews (they do not recognize the rights of Israelis to exist). It is not anywhere near as bad as Nazi Germany, but it is rather antisemitic.
"Not to mention the fake Iraqis overturning incubators"
What were these fake Iraqis really, once you took their "Iraqi costumes" off. Were they Bildeburger agitprop agents? Or was it Mossad guys?
Don't blame Durga. I voted for Centauri.
What?!? Einstein '..only had a small armful of memorable discoveries spread over the decades of his career..'?!? Please, do your homework and THEN post. Your comment makes you sound quite like the person who posts about something they know little about. Ramanujan may or may not have been smarter than Eintein (I don't think we should be including Linus in the same league as either man, but whatever), but what counts is what each's contributions are. See Macadamizer's post for 'Big AL's contributions to human knowledge and see mamba-mamba's post for Ramanujan's contributions. Or even better, consult each man's biographies.
There is some evidence that Mileva (Einstein's wife at the time) contributed to shaping Einstein's ideas. However, her contributions were at the level that one acknowledges at the end of a scientific paper ('thanks to person X for insightful conversations'). There is no evidence she contributed fundamentally to Einstein's ideas. As for the 'accusations' (http://home.comcast.net/~xtxinc/mileva.htm), well, I guess we MUST believe it because it's on the web, right? C'mon...
How about an American being a world-class football (soccer) player such as Tim Howard, goalkeeper for the most famous team in the world -- Manchester United of England.
In any case, anyone familiar with mathematics would immediately identify "That Indian Math Guy" as Ramanujan, with no disrespect intended.
I'm still trying to figure that out, so I'm not reading any further.
In case you're wondering, the parent post was modded insightful because now people don't actually have to click on the link and risk RTFA.
I'm sure I heard a professor talk about him in Calculus, and then I read about him in several popular math books, like either Ivar Peterson's Mathematical Tourist or one of the popular books on the solving of Fermet's last theorum.
Dude, I think I can see my house from here.
Reading about Srinivasa Ramanujan reminds me of a finding a solution for the following pattern. It's very very simplistic but took me quite some time to actually figure out. See my reply for the solution.
The basic idea is you can take any number and the end result will be 4.
Here are some examples
Staring Value: Sequence
-1: 11, 6, 3, 5, 4
0: 4
1: 3, 5, 4
2: 3, 5, 4
10: 3, 5, 4
5293: 33, 11, 6, 3, 5, 4
Just count the number of letters in the number
0 - Zero 4
-1 - Negative One 11, Eleven 5 five, 4 four
5293 - Five Thousand Two Hundred Nintey Three 33, Thirty Three 11, Eleven 5, Five 4
[Descartes called numbers of the form a + bj "imaginaire"] because they could not be plotted using his cartesian coordinate system
"Could not be plotted" or "could not be plotted by Descartes"? Look at any Laplace transform or z-transform of an analog or digital filter. You'll see poles and zeroes plotted as Xs and Os centered at points (x, y), where each pole or zero corresponds to x + yj in the s- or z-plane. In general, the plot of a single complex number n on a cartesian plane is a bullet centered at (Re(n), Im(n)).
Even in large systems it is theoretically possible to see it violated, it would just take longer than the existence of the universe for you to ever observe such a violation.
?-|||-----x<*))))><
Let me see if i get this right: You say that what matters is the quality of the original post, and not the content of the post?!!!? IMHO you should no longer take up precious bandwidth on ridiculous statements like that which have little (yeah, right) basis for being rational. Please go to an alternative such as msn.... And to think that the initial part of your post was actually sensible.... Was the latter part a brain fart? Insightful, my dead granny's behind.
For every present, there is a past
In case you're wondering, the parent post was modded insightful because now people don't actually have to click on the link and risk RTFA.
Now that is pure genious.
Now, I did get my BS in math, read The Man Who Knew Infinity, and so know who he was, but regardless.
That was great.
Muhutma Ghandi described his experience about the same time in England, from a similar Hindu culture.
Ghandi nearly starved in England.
England at that time wasn't blessed with good Indian resturants on every block.
The supply of fruits and veggies at that time was pathetic, particularly in winter.
Attempting to be vegetarian in such an environment is dangerous. But wait- there's more.
The English diet depends heavily on milk, and most Indians cannot drink fresh milk. That is why, in Indian cooking the milk is always served as yogurt, clarified butter, cheese or ice-cream.
Ghandi had terrible stomach pain when he tried.
Just learning to deal with the stomach pain doesn't help- a person without the lactase enzyme cannot gain nutrition by trying to drink milk.
TB rarely kills a healthy person, but with a poor diet or weak immune system (AIDS) it is lethal.
How about an American being a world-class football (soccer) player such as Tim Howard, goalkeeper for the most famous team in the world -- Manchester United of England.
He was talking about sports, not games. Soccer is so boring the fans fight each other to liven things up.
-1 Uncomfortable Truth
Now that I know what you are talking about it is a fun puzzle to solve it turns-out :)
... + 2(p+q) - 1 = (p+q)^2 = p^2 + 2pq + q^2 ... + 2(p-q) - 1 = (p-q)^2 = p^2 - 2pq + q^2
... + 2(p+q) - 1 = 4pq
:)
./? No it is a cute puzzle, fun to solve, but please do not present it as if it were some earth shattering discovery in mathematics. And when you make a simple mistake don't start attacking the terminology of someone else when they honestly don't see what you are talking about because of the fact that you poorly characterized the problem. Once I saw what you were talking about I had fun solving it. It was a cute puzzle as it turns-out, one that I gave my wife to work-out this morning.
Take two integers p > 1 and q > 1.
1 + 3 +
1 + 3 +
Subtract the bottom from the top:
2(p-q) - 1 +
That is your longer non-trivial way to write 4pq as a sum of consecutive odds.
The trick is to realize that the sum of consecutive odds is a square. It is a simple formula that people can remember and probably every one proved via induction when they learned induction. The easy way to remember it is like this:
X
YZ
XY
YYX
ZZY
ZZY
Maybe my lame diagrams above actually make it harder to visualize
But honestly now I remember why I got a degree in CS in addition to Math. It was the small bunch of antisocial pricks in the Math program that made even the worst of the CS types fun to be around in comparison. Why did you go out of your way and attack me with your reply? Look I solved this in no time in my head when I was making the bed this morning. Does that deserve to be an article on
Really I am not trying to be mean here. Probably no one has told you yet about how it counts to be nice. If you do not keep it in check what will happen? Is it your goal to be one of the smart-a*s profs that make their students feel like idiots? Wouldn't you rather be one of those that makes them feel intelligent - the kind that let them see that they are learning?
Cute puzzle, thanks :)
:) Also notice that if you consider the differences between (x±y)^2 in general you have a nice little pattern :)
:)
26^2 = (25+1)^2 = 25^2 + 2*25 + 1
24^2 = (25-1)^2 = 25^2 - 2*25 + 1
Subtract them:
26^2 - 24^2 = 4*25 = 100
Again, cute
Incidentally my first reaction was, "they are 100 apart because 10, 24, 26 is a Pythagorean triple," but I thought there might be more too it than that. Anyway I suppose that was the 'Greek math guy' you were referring to
Now that I know what you are talking about it is a fun puzzle to solve it turns-out :)
./?
I see you went from p and q to 4pq. I tripped across this little puzzle going from 4pq to p and q. I realized that 4pq is always a sequence of odd numbers, but there isn't an easy way that I know of to determine the start and end of the series without either p or q (only having 4pq). So, I quit that and went on to other things.
Why did you go out of your way and attack me with your reply?
I didn't realize that what I said would be taken as an attack. I never said anything like 'Hey idiot...' I just said that you were using what I would call a 'set' and I was using a 'sequence'.
Does that deserve to be an article on
Now, you get to the whole point of the post. It was not to announce a great discovery in mathematics. It was to make a joke about having slashdot articles about 'some guy' who solved a math puzzle. The blurb actually referred to him as 'some guy'. I was poking fun at slashdot, not mathematics. I hadn't really intended for anyone to take my simple math puzzle seriously.
The previous comment is purposely vague and generalized, but all of the facts are completely true.
So maybe you should say "If I was a short Italian dude from the past where would I go?"
"sweet dreams are made of this..."
Now I see how this was a joke and I feel really stupid and embarrassed about that. Sorry about that, I guess I do not have a keen sense of humor. Also I have a - where there should be a + in one place and I call 1 a prime in another, so that serves me right. To be honest, the whole 'Indian math guy' bit bothered me too. At least I got a nice puzzle out of it :)
Bernie Worrell, a modern day music genius could do the same kinds of things.
Excuse me for not being a Linus fanboy, but Linus is NOT in the same league as Einstein. I'm surprised they're mentioned in the same sentence. When Linus dies, nobody will be falling over themselves to dissect his brain.
/. community and the extent to which their respective names are known here. Your dad may not've tried to unify his own theories with those of Newton (well, maybe after a pint or two), but that doesn't mean you can't hold him in the same esteem. The same goes for anyone you respect.
It's not the caliber of their accomplishments, rather the respect they get from the
We now have confirmed reports from an informed Orange County minister that Ethel is still an active communist.
Only on Slashdot would there be a dude who argues that _Einstein's_ number of discoveries was mediocre ;)
...oh. :-P
Relative to other geniuses, of course... *ow!*
Seriously! I mean, how many patches has Big Al submitted to the kernel? Huh? How many?
That's what I thought. He must be a crackpot, and therefore, terminated.
We now have confirmed reports from an informed Orange County minister that Ethel is still an active communist.
You're right--the arthur's one of my white-supremacist buddies; inbetween linchings last week, he showed me a rough draft of the article he submitted and I said, "Now hold on for a minute, Jethro--did you just refer to Ramanujan by his name?"
/. community, I've never said his name without explaining. Grow up, and realized the ommission of non-known names in favor of a title more generic title is not an American phenomenon, nor is it necessarily bad. As many other posters pointed out, what're you more likely to remember: Ramanujan, or an Indian Math Guy? I'll take my fly down so when you get here you have one less step to go through.
Seriously, how the hell can any one of you self-righteous PC crackpots get off on the notion that it was intentionally ommited? As another posted out, perhaps the arthur simply forgot how to spell his name and was too lazy to look it back up. I'll agree that the name should've been in there somewhere, but christ--none of you would be bitching if someone referred to the scrawnly white loner from the boonies who invented TV. His name was Filo T. Farnsworth, and even though he, too, was one of the greatest minds of the early 20th century, I doubt most people here have heard of him. Outside of anyone in the
We now have confirmed reports from an informed Orange County minister that Ethel is still an active communist.
Wow, you have some very subtle language there. Yes, it "can be" a hate crime, and it "can be" more serious, but it has to be determined that it was a hate crime.
The distinction much more often made is whether a murder is first, second, or third degree.
You don't seem to read the posts carefully either, no wonder you are so ignorant!! There is no Indian grad student involved anywhere!!! The post refers to a mathematical problem posed by the great mathematician Srinivas Ramanujam, one of the greatest minds of the 20th century!!!! And now a grad student called Karl Mahlburg, at the University of Wisconsin in Madison, US, is claiming to have found a solution. If you are unaware of the name of Ramanujam, better remain quiet instead of advertising your ignorance and callous attitude.